Now, I drew many diagrams and the most accurate to me looked like this one lol. I got the right answers using this diagram but I don't know if it's correct and if it is why is O at the position of the hexagon it is?

(Original post by Chittesh14)
Hello guys, I don't understand how to do this question really.

Question :

Now, I drew many diagrams and the most accurate to me looked like this one lol. I got the right answers using this diagram but I don't know if it's correct and if it is why is O at the position of the hexagon it is?

Also, why is OC = 2AB... that also makes no sense to me :/.

There is a lot of symmetry in a regular hexagon. One useful fact is that a regular hexagon can be divided into 6 equilateral triangles.

Try marking the centre of the hexagon then draw in these 6 triangles and you should end up with 12 lines on your diagram which all have equal length. Hopefully that will help you see why the longest diagonals of the hexagon e.g. OC are twice the length of the edges e.g. AB. Also, all these lines on the diagram will hopefully help with looking for the vector pathways.

It shouldn't matter which corner is your 'O'. Since the vector pathways will always be the same, you can mark 'O' on any of the corners.

An important fact here is that a regular hexagon can be thought of as 6 equilateral triangles, like this.
From this diagram, you should be able to see how to find the vectors, since if you can find one vector for each of the 3 sides of one of the triangles, you can add/subtract these vectors to find any direction from one point to another.

(Original post by notnek)
There is a lot of symmetry in a regular hexagon. One useful fact is that a regular hexagon can be divided into 6 equilateral triangles.

Try marking the centre of the hexagon then draw in these 6 triangles and you should end up with 12 lines on your diagram which all have equal length. Hopefully that will help you see why the longest diagonals of the hexagon e.g. OC are twice the length of the edges e.g. AB. Also, all these lines on the diagram will hopefully help with looking for the vector pathways.

It shouldn't matter which corner is your 'O'. Since the vector pathways will always be the same, you can mark 'O' on any of the corners.

Thanks! Yes, I just realised that as long as the order is correct, the position of O does not matter lol. That's what I was trying - equilateral triangles but I guess my diagram was inaccurate :/. Thank you so much !

(Original post by lizardlizard)
An important fact here is that a regular hexagon can be thought of as 6 equilateral triangles, like this.
From this diagram, you should be able to see how to find the vectors, since if you can find one vector for each of the 3 sides of one of the triangles, you can add/subtract these vectors to find any direction from one point to another.

Thanks buddy, I got the question right anyway lol I knew the part after that - one point to the other because it was simple vectors I was just stupid enough to not realise the equilateral triangles stuff -_-.